Dynamical analysis of a nonlocal delays spatial malaria model with Wolbachia-infected male mosquitoes release

Malaria continues to pose a considerable threat to global health. This study investigates the use of releasing Wolbachia-infected male mosquitoes as a method to mitigate the spread of malaria. We have formulated a reaction-diffusion model with nonlocal delays that includes the Wolbachia release strategy. The basic reproduction number $R_0$ is defined within our model framework, serving as a critical threshold parameter that dictates the dynamic behavior of the model. A thorough dynamic analysis of the model reveals that when $R_0<1$, a globally attractive infection-free steady state is established. In contrast, if $R_0>1$, the disease persists uniformly. Numerical simulations are conducted to validate the theoretical results and to further illustrate the effectiveness of the Wolbachia release strategy on transmission and control of malaria. These simulations underscore the potential of using Wolbachia-infected male mosquitoes to significantly reduce spread of malaria.